Problem: $\overline{BC} = 7$ $\overline{AC} = {?}$ $A$ $C$ $B$ $?$ $7$ $ \sin( \angle BAC ) = \frac{7\sqrt{74} }{74}, \cos( \angle BAC ) = \frac{5\sqrt{74} }{74}, \tan( \angle BAC ) = \dfrac{7}{5}$
Solution: $\overline{BC}$ is the opposite to $\angle BAC$ $\overline{AC}$ is adjacent to $\angle BAC$ SOH CAH TOA We know the opposite side and need to solve for the adjacent side so we can use the tan function (TOA) $ \tan( \angle BAC ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\overline{BC}}{\overline{AC}}= \frac{7}{\overline{AC}} $ $ \overline{AC}=\frac{7}{\tan( \angle BAC )} = \frac{7}{\dfrac{7}{5}} = 5$